Piezoelectric resonator having mesa type piezoelectric vibrating element

ABSTRACT

A vibrating element includes: an element plate that has a vibrating portion that performs thickness-shear vibration, a peripheral portion that is integrally formed with the vibrating portion, and a protruding portion that is provided at the peripheral portion; and an excitation electrode that is provided at the vibrating portion. When a side length of the vibrating portion is Mx, when a side length of the excitation electrode is Ex, and when a wavelength of flexure vibrations of the element plate is λ, the relationship of (Mx−Ex)/2=λ/2, and Mx/2={(A/2)+(¼)}λ (where, A is a positive integer) is satisfied, and when a length of the protruding portion is Dx, and when a distance between the vibrating portion and the protruding portion is Sx, the relationship of Dx=λ/2)×m, and (λ/2)×n−0.1λ≦Sx≦(λ/2)×n+0.1λ (where m and n are positive integers) is satisfied.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation patent application of U.S. application Ser. No.12/909,254 filed Oct. 21, 2010, which claims priority to Japanese PatentApplication No. 2009-246902, filed Oct. 27, 2009 all of which areexpressly incorporated by reference herein.

BACKGROUND

1. Technical Field

The present invention relates to a piezoelectric resonator and inparticular, to a piezoelectric resonator having a mesa typepiezoelectric vibrating element in which the thickness of the vibratingportion is larger than that of the peripheral portion.

2. Related Art

A mesa type piezoelectric vibrating element is known as a form of apiezoelectric vibrating element which can keep vibration energy thereinand which has high productivity, the form being based on a bevel orconvex type piezoelectric vibrating element.

In the mesa type piezoelectric vibrating element which has a leveldifference on the boundary of the vibrating portion and the peripheralportion, however, spurious vibrations, such as flexure vibrations whichare unnecessary vibrations, increase with the influence of the leveldifference. Under such a background, JP-A-2006-340023 discloses atechnique of suppressing spurious vibration by optimizing the positionof a stepped portion between a vibrating portion and a peripheralportion.

Moreover, JP-A-2008-263387 discloses a technique of suppressing spuriousvibration and reducing the CI value by optimizing the size (depth) of astepped portion in addition to the position of the stepped portion.Moreover, JP-A-2008-306594 discloses a technique of improving the effectof spurious vibration suppression by extending the formation position ofan excitation electrode up to a peripheral portion with a smallthickness and setting the end of the excitation electrode at theposition of a valley of unnecessary vibration.

Thus, for a piezoelectric resonator which adopts a mesa typepiezoelectric vibrating element, various techniques have been proposedwhich suppress flexure vibrations by optimizing the position of the endedge of a mesa portion, that is, a thick portion or the position of anend edge of an excitation electrode on the basis of the relationshipwith the displacement of flexure vibrations.

However, as disclosed in JP-A-2008-263387, the CI value can be decreasedas the rate of digging quantity of the thick portion is increased, butthere is no change in the CI value if the rate of digging quantityexceeds a predetermined range. Depending on the situation, a phenomenonoccurs in which the CI value increases (deteriorates). In order to solvethis phenomenon, JP-A-10-308645 discloses a technique capable ofensuring the digging quantity (increasing the thickness of a steppedportion) and reducing the CI value by forming a mesa portion withmultiple steps.

As disclosed in JP-A-2006-340023, JP-A-2008-263387, JP-A-2008-306594,and JP-A-10-308645, the mesa type structure can suppress an unnecessarywave by specifying the position of the stepped portion. Moreover, the CIvalue of principal vibration can be decreased as the rate of diggingquantity of the stepped portion is increased, but deterioration of theCI value, that is, the phenomenon that the CI value increases occurs ifthe rate of digging quantity exceeds a predetermined value. Whenmanufacturing errors and the like are taken into consideration, it isdifficult to practically increase the digging quantity up to thethreshold value.

Moreover, in the configuration disclosed in JP-A-10-308645 in which amesa portion is formed to have multiple steps in order to increase therelative digging quantity, the CI value may be reduced, but the photoprocess for forming the mesa portion with multiple steps is increased.As a result, there is concern regarding a situation where theproductivity decreases markedly.

SUMMARY

An advantage of some aspects of the invention is to provide apiezoelectric resonator which has high productivity and which does notcause an increase in the CI value even if the digging quantity of a mesaportion is set to be larger than that in the related art.

The invention can be embodied as the following forms or applicationexamples.

APPLICATION EXAMPLE 1

This application example of the invention is directed to a piezoelectricresonator including: a piezoelectric plate of which thickness-shearvibration is the principal vibration and which has a vibrating portionthat is surrounded by a peripheral portion and has a larger thicknessthan the peripheral portion; and an excitation electrode disposed on aprincipal surface of the piezoelectric plate. Both the long side of thevibrating portion and the long side of the excitation electrode areparallel to the long side of the piezoelectric plate. Assuming that thelong side length of the piezoelectric plate is X, the thickness of thevibrating portion is t, the long side length of the vibrating portion isMx, the long side length of the excitation electrode is Ex, and thewavelength of flexure vibrations occurring in the longitudinal directionof the piezoelectric plate is λ, the following relationship issatisfied.

λ/2=(1.332/f)−0.0024 (where, f is a resonance frequency of apiezoelectric resonator)

(Mx−Ex)/2=λ/2

Mx/2={ (A/2)+(¼)}λ (where, A is 1, 2, 3, . . . (positive integer))

X≧20t

A protruding portion, which is disposed on an extension line of thevibrating portion in the longitudinal direction so as to be parallel tothe short side direction of the vibrating portion, is provided.

Assuming that the length of the protruding portion in the displacementdirection of the principal vibration is Dx, the relationship ofDx=(λ/2)×m (where, m=1, 2, 3, . . . (positive integer)) is satisfied.Assuming that the distance between the vibrating portion and theprotruding portion is Sx, the relationship of Sx=(λ/2)×n±0.1λ (where,n=1, 2, 3, . . . (positive integer)) is satisfied.

The piezoelectric resonator with such characteristics has highproductivity and does not cause an increase in the CI value even if thedigging quantity of a mesa portion is set to be larger than that in therelated art.

APPLICATION EXAMPLE 2

According to this application example of the invention, in thepiezoelectric resonator according to Application Example of theinvention, the excitation electrode is provided to extend from theprincipal surface of the vibrating portion to the peripheral portionlocated between the protruding portions and a distance L1 from thevibrating portion to an end edge of the excitation electrode, which isprovided to extend up to the peripheral portion, satisfies therelationship of L1=(λ/2)×p (where, p=1, 2, 3, . . . (positive integer)).

Also in the piezoelectric resonator with such characteristics, the sameeffects as in the piezoelectric resonator with the characteristicsdescribed above can be obtained.

APPLICATION EXAMPLE 3

According to this application example of the invention, in thepiezoelectric resonator according to Application Example 1 or 2 of theinvention, the piezoelectric plate is a quartz crystal plate and astepped portion between the vibrating portion and the peripheral portionand a stepped portion between the peripheral portion and the protrudingportion each have inclined surfaces. It is preferable that the size ofthe vibrating portion, the distance from the vibrating portion to theprotruding portion, and the size of the protruding portion are set withthe middle of the inclined surface as a reference.

Also in the piezoelectric resonator with such characteristics, areference for setting the size can be acquired even in the case offorming a piezoelectric vibrating element by wet etching.

APPLICATION EXAMPLE 4

According to this application example of the invention, in thepiezoelectric resonator according to any one of Application Examples 1to 3 of the invention, it is preferable that the protruding portion isprovided at only one end side of the vibrating portion in thelongitudinal direction.

Also in the case of mounting a piezoelectric vibrating element with suchcharacteristics, the same effects as in the piezoelectric resonator withthe characteristics described above can be obtained.

APPLICATION EXAMPLE 5

According to this application example of the invention, in thepiezoelectric resonator according to any one of Application Examples 1to 3 of the invention, the short side length of the protruding portionis set to be equal to the short side length of the vibrating portion.

With such a characteristic, it becomes possible to suppress the flexurevibration occurring at least in the range of the vibrating portion.

APPLICATION EXAMPLE 6

According to this application example of the invention, in thepiezoelectric resonator according to any one of Application Examples 1to 5 of the invention, the height of the vibrating portion and a heightof the protruding portion from the peripheral portion as a reference areequal.

With such a characteristic, formation of the protruding portion andformation of the vibrating portion can be realized through a one-timeetching process. Therefore, since productivity of the piezoelectricvibrating element can be improved, productivity of the piezoelectricresonator itself can also be improved.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIGS. 1A and 1B are views showing the configuration of a piezoelectricresonator according to a first embodiment.

FIG. 2 is a view for defining the size of each portion in apiezoelectric vibrating element in the first embodiment.

FIG. 3 is a view showing the relationship between each portion of apiezoelectric vibrating element and displacement of flexure vibration.

FIG. 4 is a graph showing the relationship between a change in the rateof mesa digging quantity and a change in the CI value.

FIGS. 5A and 5B are views for explaining an increase in the CI valueaccording to a change in the distance between a vibrating portion and aprotruding portion and the allowable range.

FIGS. 6A and 6B are views showing the configuration of a piezoelectricresonator according to a second embodiment.

FIG. 7 is a view for defining the size of each portion in apiezoelectric vibrating element in the second embodiment.

FIG. 8 is a graph showing a simulation for proving the effect in thepiezoelectric resonator according to the second embodiment.

FIG. 9 is a view showing the configuration of a piezoelectric resonatoraccording to a third embodiment.

FIG. 10 is a graph showing a simulation for proving the effect in thepiezoelectric resonator according to the third embodiment.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, a piezoelectric resonator according to an embodiment of theinvention will be described in detail with reference to the accompanyingdrawings. First, a piezoelectric resonator according to a firstembodiment of the invention will be described with reference to FIGS. 1Aand 1B. In addition, FIG. 1A is a view showing the configuration of apiezoelectric resonator when viewed from the front side, and FIG. 1B isa view showing the planar configuration in a state where a lid isremoved.

A piezoelectric resonator 10 according to the present embodimentincludes a piezoelectric vibrating element 12 and a package 30 as maincomponents. The piezoelectric vibrating element 12 is formed by a quartzcrystal plate (piezoelectric plate) which is cut at a cut angle calledAT cut or BT cut and which is excited by thickness-shear vibration asmain vibration. Moreover, in the quartz crystal plate (piezoelectricvibrating element 12), a side parallel to the X axis of the quartzcrystal is set as a long side, a side parallel to the Z′ axis of thequartz crystal is set as a short side, and the thickness direction ofthe quartz crystal plate is assumed to be parallel to the Y′ axis.

The piezoelectric vibrating element 12 formed by such a quartz crystalplate includes a thick portion (vibrating portion) 14, a thin portion(peripheral portion) 16, a protruding portion 18, and an electrode film20. The thick portion 14 is defined by relationship with the thinportion 16, and the thin portion 16 is provided around the thick portion14. In the present embodiment, a shape unified by overlapping the thickportion 14 with a rectangular flat surface on the rectangular flatplate, which has a long side in a direction parallel to the X axis ofthe quartz crystal as described above, so that their long sides areparallel to each other is formed by one element plate. In addition, thethick portion 14 is provided on both principal surfaces of the thinportion 16 so as to protrude therefrom.

The protruding portion 18 is provided extending in a directionperpendicular to the direction parallel to the long side of the thickportion 14 provided as described above, that is, in a directionperpendicular to the direction parallel to the displacement direction(X-axis direction in the drawing) of main vibration in the thick portion14. With the surface of the thin portion 16 as a reference, thethickness of the protruding portion 18 in the Y′ direction has the sameheight (digging quantity) as the thickness of the thick portion 14 inthe Y′-axis direction. In addition, the extending direction of theprotruding portion 18 is set to be parallel to the width direction(Z′-axis direction in the drawing) of the thick portion 14. In thepresent embodiment, the length of the protruding portion 18 in theZ′-axis direction is the same as the width of the thick portion 14.

The electrode film 20 has an excitation electrode 22, a lead-outelectrode 24 and an input/output electrode 26. In the presentembodiment, the excitation electrode 22 is formed on both of one surface14 a and the other surface 14 b of the thick portion 14. Moreover,although the shape of the excitation electrode 22 is not particularlylimited, the shape of the excitation electrode 22 is similar to theplanar shape of the thick portion 14 as shown in FIG. 1B in the presentembodiment. The input/output electrode 26 is provided on the othersurface of one end (called a base side end) of the thin portion 16 inthe longitudinal direction. The lead-out electrode 24 is lead out sothat the excitation electrode 22, which is formed on the one surface andthe other surface of the thick portion 14, and the input/outputelectrode 26, which is formed on the other surface at the base side endof the thin portion 16, are electrically connected to each other.

In the piezoelectric vibrating element 12 with such a basicconfiguration, the wavelength λ of flexure vibration which is anunnecessary wave is decided by the plate thickness t (mm) of the thickportion 14 formed as a vibrating portion. Here, the relationship betweenthe plate thickness t (mm) of the thick portion 14 and the frequency f(MHz) of thickness-shear vibration, which is principal vibration of thepiezoelectric vibrating element 12, may be expressed by Expression 1given below.

f=k/t   [Expression 1]

In addition, a frequency constant k is set to 1.670 MHz·mm when thequartz crystal plate is AT cut and 2.560 MHz·mm when the quartz crystalplate is BT cut. Moreover, if the amount of frequency reduction by anelectrode is taken into consideration, Expression 2 is satisfied, sothat the relationship between the wavelength λ (mm) of flexure vibrationand the plate thickness t (mm) of the thick portion 14 can be expressed.

λ/t=(1.332/f)−0.0024  [Expression 2]

As disclosed in JP-A-2006-340023 or JP-A-2008-306594, it is known that aflexure vibration component is suppressed when both the end edge of thethick portion 14 and the end edge of the excitation electrode 22 arelocated at the valley of a waveform of flexure vibration (flexuredisplacement). Then, if a dimension for matching the end edge of thethick portion 14 or the end edge of the excitation electrode 22 with theposition of the valley of the flexure displacement is expressed on thebasis of the relationship with the waveform λ of flexure vibration,Expression 3 is obtained. From FIG. 2, the long side length of theexcitation electrode 22 is set to Ex (mm) and the long side length ofthe thick portion 14 is set to Mx (mm).

(Mx−Ex)/2=λ/2   [Expression 3]

Moreover, in the case of the relationship example expressed byExpression 3, it is assumed that the middle position of the thickportion 14 and the middle position of the excitation electrode 22 areequal.

In addition, the relationship between the long side length Mx (mm) ofthe thick portion and the wavelength λ (mm) may be expressed byExpression 4.

Mx/2={(A/2)+(¼)}λ (where, A is a positive integer)  [Expression 4]

In addition, the above relationship expression is based on theassumption that the long side length X (mm) of a quartz crystal plate issufficiently larger than the thickness t (mm) of the thick portion 14.Specifically, it is preferable to satisfy the relationship of Expression5.

X≧20t [Expression 5]

According to the piezoelectric vibrating element 12 which satisfies theabove relationship, the flexure vibration component is suppressed.However, if only such a relationship is satisfied, it is known that theCI value is increased markedly if the digging quantity of the thickportion 14 exceeds a predetermined rate.

Therefore, in the present embodiment, the protruding portion 18 isprovided in the thin portion 16, and an end edge of the protrudingportion 18 is made to match the valley of flexure displacement regardingthe relationship between the protruding portion 18 and the flexurevibrations, as shown in FIGS. 2 and 3.

In order to satisfy such a relationship, it is preferable to calculatethe length Dx (mm) of the protruding portion 18 in the X-axis directionand the distance Sx (mm) from the end edge of the thick portion 14 tothe end edge of the protruding portion 18 on the basis of therelationship with the wavelength λ of the flexure displacement and tosatisfy this relationship.

The length Dx (mm) of the protruding portion 18 in the X-axis directioncalculated as described above may be expressed by Expression 6.

Dx=(λ/2)×m (where, m is a positive integer)  [Expression 6]

In addition, the distance Sx (mm) from the end edge of the thick portion14 to the end edge of the protruding portion 18 in the piezoelectricvibrating element 12 may be expressed by Expression 7.

Sx=(λ/2)×n±0.1λ (where, n is a positive integer)  [Expression 7]

By satisfying all of such relationships, all of the end edge of thethick portion 14, the end edge of the excitation electrode 22, and theend edge of the protruding portion 18 are located at the valley offlexure displacement. Accordingly, flexure vibration can be suppressed.

In addition, an increase in the CI value when setting the height(digging quantity) of the thick portion 14 to be large can be suppressedby adopting such a configuration. FIG. 4 shows changes of the CI valuewith a difference in the rate of digging quantity (Md) in a mesa typepiezoelectric resonator (related art), in which a protruding portion isnot provided and the end edge of a thick portion and the end edge of anexcitation electrode are matched with a valley of flexure displacement,and a mesa type piezoelectric resonator with a protruding portionaccording to the present embodiment (invention of this application).Referring to FIG. 4, if the known structure and the invention of thisapplication are compared for the same Md, it can be seen that the CIvalue tends to decrease by providing the protruding portion and it ismost effective when the length of a long side of a piezoelectric plateis set to X=1.375 mm.

As can be seen from FIG. 4, in the piezoelectric resonator according tothe known technique, it can be checked that the CI value increases if Mdincreases from 15% (rate with respect to the thickness t) to 20% for allsizes (X size). On the other hand, in the piezoelectric vibratingelement 12 of the invention of this application, it can be seen that ifthe value of Md increases from 15% to 20%, there is almost no increasein the CI value compared with the case of Md=15% (in the case of X=1.375mm), and the CI value slightly increases compared with the case ofMd=15% (in the case of X=1.385 mm). However, there is a condition inwhich the CI value is further reduced (in the case of X=1.365 mm).

Thus, according to the piezoelectric resonator 10 of the presentembodiment which adopts the piezoelectric vibrating element 12 thatsatisfies the above configuration, an increase in the CI value can besuppressed even if the rate (Md) of digging quantity of the thickportion 14 is set to be large. For this reason, mass production of apiezoelectric resonator with a rate of digging quantity capable ofobtaining a desired CI value becomes possible without taking intoconsideration an increase in the CI value caused by overetching.

Here, if shaping of a quartz crystal plate is performed by wet etching(hereinafter, simply called etching), the sectional surface may beinclined due to anisotropy of the quartz crystal direction. In the caseof an AT-cut quartz crystal plate used in the present embodiment, astepped portion between the thick portion 14 and the thin portion 16becomes an inclined surface as shown in FIG. 3. In the presentembodiment, however, the midpoint of an inclined surface generated dueto the anisotropy of the quartz crystal direction is set as an end edge,and this portion is formed so as to match the valley of flexuredisplacement. Thus, it is possible to realize a piezoelectric resonatorwith good CI characteristics.

Moreover, in the piezoelectric vibrating element 12 according to thepresent embodiment, it is possible to have an allowance of about ±0.1λin the arrangement relationship of the thick portion 14 and theprotruding portion 18. This can be understood from the evaluationresults of CI characteristics shown in FIGS. 5A and 5B. Specifically, asshown in FIG. 5A, if the distance between the thick portion 14 and theprotruding portion 18 is changed, the CI value increases by about 10 Ωas the distance between the thick portion 14 and the protruding portion18 changes by 10 μm. In the piezoelectric resonator exemplified in FIG.5A, the frequency f is set to 24 MHz, the X size is set to 1.375 mm, Mdis set to 20%, and the wavelength λ of flexure vibration is set to about107 μm. In addition, the graph on the right side having a value betweenthe mesa end and the protruding portion, which indicates the distancefrom the thick portion 14 to the protruding portion 18 and which is avalue closest to twice the value of protruding portion width Dxindicating the width of the protruding portion 18, is set as a referencegraph in FIG. 5A.

If the right graph in FIG. 5A is used as a reference, the CI value whenthe value (distance between the mesa end and the protruding portion) ofSx has changed by 10 μm is better than the CI value (refer to FIG. 4) ofa piezoelectric resonator in the known structure, and there is anincrease in the CI value when the amount of change is 20 μm.Accordingly, it could be seen that the amount of change of 10 μm was asubstantially allowable range.

Moreover, regarding a piezoelectric resonator in which the frequency fis set to 26 MHz, an increase in the CI value is not observed even ifthe position of a protruding portion changes by 10 μm, as shown in FIG.5B. Moreover, in FIG. 5B, the middle graph in which the distance betweenthe mesa end and the protruding portion is equal to the value of theprotruding portion width is set as a reference. In addition, thewavelength λ of flexure vibration is about 98 μm.

Based on such simulation evaluation, it is thought that the value of Sxhardly affects an increase in the CI value even if an error of about ±10μm occurs in the piezoelectric resonator according to the presentembodiment. In the present embodiment, therefore, the allowance of Sxwas set to ±10 μm. In addition, since the wavelength X of flexuredisplacement in the piezoelectric resonator of f=24 MHz is about 107 μmand the wavelength λ of flexure displacement in the piezoelectricresonator of f=26 MHz is about 98 μm, Expression 8 is satisfied assumingthat the wavelength of flexure displacement in these piezoelectricresonators is about 100 μm.

±10(μm)=±0.1λ  [Expression 8]

From this, in Expression 7, the allowance is expressed by therelationship with the wavelength λ.

Next, a package which forms a piezoelectric resonator includes a packagebase and a lid. A package base 32 shown in FIGS. 1A and 1B has arectangular box shape and includes an internal mounting terminal 38 onthe internal bottom surface and an external terminal 40 on the externalbottom surface. In addition, the internal mounting terminal 38 and theexternal mounting terminal 40 are electrically connected to each otherthrough a circuit pattern (not shown).

The piezoelectric vibrating element 12 is mounted in the package base 32using a bonding material 42, such as a conductive adhesive. In themounting process, the bonding material is applied on the internalmounting terminal 38 of the package base 32, and the piezoelectricvibrating element 12 is mounted such that an I/O electrode is located onthe applied bonding material 42.

As shown in FIGS. 1A and 1B, when the boxed-shaped package base 32 isadopted, a so-called lid which has a flat plate shape is adopted as alid 34. The lid 34 is bonded to the package base 32 through a seam ring36 as a soldering material.

The piezoelectric resonator 10 with such a configuration is manufacturedthrough the following processes.

First, a corrosion-resistant film is formed on an AT cut or BT cutquartz crystal plate. Then, a resist film is formed to cover thecorrosion-resistant film, and patterning processing for removing theresist film excluding the thick portion 14 and the protruding portion 18is performed. The corrosion-resistant film is etched using the patternedresist film as a mask, and then the quartz crystal plate is etched usingthe resist film and the corrosion-resistant film as a mask.

In addition, since the digging quantity of quartz crystal by etching andthe angle of the quartz crystal face formed by anisotropy of the quartzcrystal direction are known, patterning of the resist film at the timeof etching is performed in consideration thereof.

The resist film and the corrosion-resistant film are peeled off from thequartz crystal plate for which the appearance formation using etchinghas ended, and a metal film for forming the excitation electrode 22, theinput/output electrode 26, and the lead-out electrode 24 is formed.Forming a metal film is preferably performed by vapor deposition,sputtering, and the like.

After forming the metal film, the metal film is covered with a resistfilm and the resist film is patterned according to the shapes of theexcitation electrode 22, the input/output electrode 26, and the lead-outelectrode 24. After patterning the resist film, the electrode film 20 isformed by etching the metal film using the patterned resist film as amask. As a result, the piezoelectric vibrating element 12 is obtained.

Then, the resist film is peeled off, and the piezoelectric vibratingelement 12 is mounted in the package base formed separately. Aftermounting the piezoelectric vibrating element 12 in the package base 32,an opening of the package base 32 is sealed with the lid 34. Thus, thepiezoelectric resonator 10 is formed.

The piezoelectric resonator 10 with such a configuration has highproductivity and can suppress an increase in the CI value even if thedigging quantity of a mesa portion (thick portion 14) is set to belarger than that in the related art. Therefore, the rate Md of diggingquantity can be set to the appropriate value, at which the CI value issatisfactory, regardless of overetching.

Moreover, in the embodiment described above, the package 30 which formsthe piezoelectric resonator 10 is formed by the box-shaped package base32 and the flat-plate-shaped lid 34. However, the piezoelectricresonator 10 according to the embodiment of the invention may have apackage base with a flat plate shape and a so-called capped lid with abox shape.

Next, a piezoelectric resonator according to a second embodiment of theinvention will be described in detail with reference to FIGS. 6A and 6B.In addition, most of the configuration of the piezoelectric resonatoraccording to the present embodiment is the same as the piezoelectricresonator according to the first embodiment described above.Accordingly, the same components as in the first embodiment are denotedby reference numerals obtained by adding 100 to reference numerals inthe drawings in the first embodiment and a detailed explanation thereofwill be omitted. In addition, FIG. 6A is a view showing theconfiguration of a mesa type piezoelectric resonator when viewed fromthe front side, and FIG. 6B is a view showing the planar configurationin a state where a lid is removed.

In a piezoelectric resonator 110 according to the present embodiment, anexcitation electrode 122 is provided to extend up to a thin portion 116which is located on the extending line of the long side of the thickportion 114 (in the displacement direction of principal vibration).

In the present embodiment, the relationship of long side length Mx ofthe thick portion 114, long side length Ex1 of an excitation electrode,and a waveform λ of flexure displacement may be set as follows (refer toFIG. 7). First, the long side length Mx of the thick portion 114 isassumed to satisfy the relationship of Expression 4.

Next, the relationship between the long side length of the thick portion114 and the long side length Ex1 of the excitation electrode 122 isassumed to satisfy Expression 9.

Ex1=Mx+(L1+L2)  [Expression 9]

Here, end edges of L1 and L2, which are relevant to end edges of theexcitation electrode, need to be matched to the valley of flexuredisplacement as also described in the first embodiment. Accordingly, theend edges of L1 and L2 are set to satisfy the relationship ofExpressions 10, 11, and 12.

L1=(λ/2)×p (where, p is a positive integer)  [Expression 10]

L2=(λ/2)×q (where, q is a positive integer)  [Expression 11]

L2−L1=r×λ (where, r is an integer)  [Expression 11]

Regarding the relationship between a protruding portion 118 and the endedge of the excitation electrode 122, the end edge of the protrudingportion 118 and the end edge of the excitation electrode 122 may bematched by setting the relationship of L1≦Sx and L2≦Sx.

In the piezoelectric resonator 110 of the present embodiment whichsatisfies such relationships, most deterioration (increase) of the CIvalue can be suppressed even if the rate Md of the digging quantity ofthe thick portion 114 is increased, as shown in FIG. 8. Thus, also whensuch a configuration is adopted, the same effects as in thepiezoelectric resonator 10 according to the first embodiment can beobtained.

Next, a piezoelectric resonator according to a third embodiment of theinvention will be described in detail with reference to FIG. 9. Inaddition, most of the configuration of the piezoelectric resonatoraccording to the present embodiment is the same as the piezoelectricresonator according to the first embodiment described above.Accordingly, the same components as in the first embodiment are denotedby reference numerals obtained by adding 200 to reference numerals inthe drawings in the first embodiment and a detailed explanation thereofwill be omitted.

In a piezoelectric resonator 210 according to the present embodiment, aprotruding portion 218, which is provided in a thin portion 216, is onlyan end (distal side end) of the other side of the thin portion 216. Alsowhen such a configuration is adopted, end edges of a thick portion 214,an excitation electrode 222, and the protruding portion 218 are formedso as to be located at the valley of flexure displacement.

In the case of adopting such a configuration, whether or not there is aninfluence on an increase in the CI value when increasing the rate Md ofdigging quantity of the thick portion 214 becomes a problem due toproviding the protruding portion 218, which is disposed with the thickportion 214 interposed therebetween, at only the distal side end. Then,simulation of the CI value change according to a change of the rate Mdof digging quantity by the piezoelectric resonator, which has thepiezoelectric vibrating element according to the embodiment of theinvention mounted under the same conditions other than a protrudingportion provided at the base side end, is shown in FIG. 10. In FIG. 10,the graph titled “protruding at both sides” shows a change in the CIvalue of the piezoelectric resonator 10 according to the firstembodiment, and the graph titled “protruding at a single side” shows achange in the CI value of the piezoelectric resonator 210 according tothe present embodiment.

As is apparent from FIG. 10, also when the protruding portion 218 isprovided at only one side, the same effects as in the piezoelectricresonator according to the first embodiment can be obtained. Therefore,the piezoelectric resonator 210 with such a configuration can also bemade as a part of the invention.

What is claimed is:
 1. A vibrating element comprising: an element plate,the element plate including: a vibrating portion that performsthickness-shear vibration; a peripheral portion that is integrallyformed with the vibrating portion at a periphery of the vibratingportion, that has a thinner thickness than the vibrating portion, andthat is located along the periphery that is perpendicular to adisplacement direction of the thickness-shear vibration; and aprotruding portion that is provided at the peripheral portion; and anexcitation electrode that is provided at the vibrating portion, whereinwhen a side length, which is located along the displacement direction,of the vibrating portion is Mx, when a side length, which is locatedalong the displacement direction, of the excitation electrode is Ex, andwhen a wavelength of flexure vibrations, which occurs along thedisplacement direction, of the element plate is λ, the relationship of(Mx−Ex)/2=λ/2, andMx/2={(λ/2)+(¼)}λ (where, A is a positive integer) is satisfied, andwhen a length, which is located along the displacement direction, of theprotruding portion is Dx, and when a distance between the vibratingportion and the protruding portion is Sx, the relationship ofDx=(λ/2)×m, and(λ/2)×n−0.1×λ≦Sx≦(λ/2)×n+ 0.1×λ (where m and n are positive integers) issatisfied.
 2. The vibrating element according to claim 1, wherein theexcitation electrode extends to an area of the peripheral portionbetween the vibrating portion and the protruding portion, and a lengthL1 that is defined between the periphery of the vibrating portion and anedge of the extended excitation electrode on the peripheral portionsatisfies the relationship of L1=(λ/2)×p (where, p is a positiveinteger).
 3. The vibrating element according to claim 1, wherein when aside length, which is located along the displacement direction, of theelement plate is X, and when a thickness of the vibrating portion is t,the relationship ofX≧20×t is satisfied.
 4. The vibrating element according to claim 2,wherein when a side length, which is located along the displacementdirection, of the element plate is X, and when a thickness of thevibrating portion is t, the relationship ofX≧20×t is satisfied.
 5. The vibrating element according to claim 1,wherein the element plate is a quartz crystal plate, and when both astepped portion between the vibrating portion and the peripheral portionand a stepped portion between the peripheral portion and the protrudingportion have inclined surfaces, each of the following seizes is definedby setting a middle point of each of the inclined surfaces as areference point: the side length, which is located along thedisplacement direction, of the vibrating portion; the distance, which islocated along the displacement direction, between the vibrating portionand the protruding portion; and a length, which is located along thedisplacement direction, of the protruding portion.
 6. The vibratingelement according to claim 2, wherein the element plate is a quartzcrystal plate, and when both a stepped portion between the vibratingportion and the peripheral portion and a stepped portion between theperipheral portion and the protruding portion have inclined surfaces,each of the following seizes is defined by setting a middle point ofeach of the inclined surfaces as a reference point: the side length,which is located along the displacement direction, of the vibratingportion; the distance, which is located along the displacementdirection, between the vibrating portion and the protruding portion; anda length, which is located along the displacement direction, of theprotruding portion.
 7. The vibrating element according to claim 1,wherein the protruding portion is provided at only the peripheralportion located at one end side, which is located along the displacementdirection, of both end sides of the vibrating portion.
 8. The vibratingelement according to claim 2, wherein the protruding portion is providedat only the peripheral portion located at one end side, which is locatedalong the displacement direction, of both end sides of the vibratingportion.
 9. The vibrating element according to claim 1, wherein a sidelength, which is perpendicular to the displacement direction of thethickness-shear vibration, of the protruding portion is equal to a sidelength, which is perpendicular to the displacement direction of thethickness-shear vibration, of the vibrating portion.
 10. The vibratingelement according to claim 2, wherein a side length, which isperpendicular to the displacement direction of the thickness-shearvibration, of the protruding portion is equal to a side length, which isperpendicular to the displacement direction of the thickness-shearvibration, of the vibrating portion.
 11. The vibrating element accordingto claim 1, wherein a height between a top surface of the peripheralportion and a top surface of the protruding portion is equal to a heightbetween the top surface of the peripheral portion and a top surface ofthe vibrating portion.
 12. The vibrating element according to claim 2,wherein a height between a top surface of the peripheral portion and atop surface of the protruding portion is equal to a height between thetop surface of the peripheral portion and a top surface of the vibratingportion.
 13. A resonator comprising: the vibrating element according toclaim 1; and a package in which the vibrating element is assembled. 14.A resonator comprising: the vibrating element according to claim 2; anda package in which the vibrating element is assembled.